Continuous Charging Options for 400Ah 12V Battery With 3600W Inverter Load

I am currently designing a cart which carries AC powered appliances. Total wattage is around 3000 Watts. I am allowed to have one plug exiting the cart which will be plugged into a 15A/20A Receptacle.

Currently i have a DC battery powering up an inverter.

Inverter going through a breaker panel with switches. Each switch with rated current relative to the appliance (20A switch if the load is 15A)

Since i have 4 AC powered components and one DC powered i am powering that DC component from the breaker panel as well by using a Class 2 transformer as it is a low voltage component

The issue that i am having is with the DC battery. If i use a 12V battery and the inverter rated for 3600 Watts, i need 300A from the battery. a 400ah battery will discharge very fast therefore i want to wire it such that the battery is continuosly being charged through that 120Vac receptacle. I am having a hard time finding a charger that can continously charge a 400ah battery. 
Is there a better way to wire this circuit?

Thanks

 

HI

Can you show us a diagram of the connection you've made?

Hi Kevin,

Main goal is to make sure that only one plug is being exposed, rest of the wiring is done internally
I have a DC battery charger powering up a battery which is wired a DC to AC Converter providing 3600 Watts
The converted is then wired to a 2-pole main switch for protection rated at 60A
60A is then further divided into 5 individual trip switches rated 20A,20A,10A,5A and 5A
Each trip switch is wired to a separate receptacle and labelled for each component
I have 5 AC power components
One of the 5 is an adapter which is used to powered DC powered panels

Thank you

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